Aims. During the solar minimum of 2008, the value of total solar irradiance at 1 AU (TSI) was more than 0.2Wm(-2) lower than during the last minimum in 1996, indicating for the first time a directly observed long-term change. On the other hand, chromospheric indices and hence solar UV irradiance do not exhibit a similar change. Methods. Comparison of TSI with other activity parameters indicates that only the open solar magnetic field, B-R, observed from satellites at 1 AU show a similar long-term behaviour. The values at the minima correlate well and the linear fit provides a direct physical relationship between TSI and B-R during the minimum times. Results. This correlation allows an unambiguous reconstruction of TSI back in time, provided the open solar magnetic field can be determined from e. g. geomagnetic indices or cosmogenic radionucleides. Since the solar UV irradiance has no long-term trend, the mechanism for the secular change of TSI must differ from the effect of surface magnetism, as manifested by sunspots, faculae, and network which indeed explain well the intra-cycle variability of both total and spectral irradiance. Conclusions. The long-term trend of TSI is most probably caused by a global temperature change of the Sun that does not influence the UV irradiance in the same way as the surface magnetic fields.